Does the whirlwind monstrous ability (as possessed by air elementals) affect swarms?
I'd rule yes, definitely.
Why wouldn't a mass of ants/spiders/bats be tossed around by a mass of swirling wind?
Since swarms usually consist of creatures tiny & smaller, i'd say tiny creatures (such as cats) can roll for a save, diminutive and smaller (like spiders and ants) get no save.